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This study delves into metabolic rate variations in roaches based on size and temperature. Learn about isometry and proportional changes in biological dimensions. Discover how metabolic rate relates to mass and explore heart rate differences in animals.
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Today • Calculate metabolic rate using different methods – indirect calorimetry and respirometry. • Examine the effects of size on metabolic rate • Examine the effects of temperature on metabolic rate.
Isometry = body dimensions scale exactly i.e. as the height doubles the arm length doubles. Note that the surface to volume ratio changes, however. 96(16x) Surface:volume 6:1 3:1 2:1 1.5:1
With allometric change the proportions vary. Note the size of the head and eyes.
If the large roach ( 8 inches)were 4 x as long as the small one (2 inches) its surface area would be 42 times greater and its volume would be 43 time greater. The small roach would have a surface to volume ratio of 4:1 and the large roach 2:1 . The small roach would have a much more efficient absorbtive surface for digestion and respiration. If there were isometric scaling of the body, legs of the large roach would have a cross sectional area 16x greater but a volume or density 64x greater. Legs would be carrying 4 x as much weight.
Metabolic Rate = a Mb (1) where a is the log/log intercept, M is mass and b is the rate of change of metabolic rate with mass. For Mass specific rate MR/M = aM b /M = aM b-1(2) Expressing these equations as logs gives a straight line where b= the slope. For (1) log MR = log a + b(log M) For (2) log MR/M = log a +( b-1) log M
In general large animals live slower than small animals. Chicken heart rate = 300 beats/minute. Elephant heart rate = 30 beats/minute. Elephant mass = 10,000 chicken mass. Warm blooded animals die after 1-2 billion heart beats so elephant lives longer.
Rubner rule: Metabolic rate varies with mass 2/3 If length = l 1; then area is proportional to l2 and volume is proportional to l3 ; so the surface to volume ratio is l2:l3 or l 2/3 Problems : shouldn’t there be differences between ectotherms and endotherms ? Between plants and animals ? Kleibner’s Rule == Metabolic rate = mass 3/4